It will take 39.3 years for the balance of this account to reach $5000
Step-by-step explanation:
Formula for time (t)
t = [tex]\frac{ln(\frac{A}{P})}{n[ln(1+\frac{r}{n})]}[/tex]
Where:
1. A = the value of the accrued investment/loan
2. P = the principal amount
3. r = the annual interest rate (decimal)
4. n = the number of times that interest is compounded per unit t
5. t = the time the money is invested or borrowed
∵ Olga invests $3000 in an account that earns 1.3% annual interest
compounded monthly
∴ P = $3000
∴ r = 1.3% = 1.3 ÷ 100 = 0.013 ⇒ annual interest
∴ n = 12 ⇒ compounded monthly
∵ The account will reach $5000
∴ A = 5000
- Substitute these values in the rule above
∴ t = [tex]\frac{ln(\frac{5000}{3000})}{12[ln(1+\frac{0.013}{12})]}[/tex]
∴ t = 39.3 years
It will take 39.3 years for the balance of this account to reach $5000
Learn more:
You can learn more about interest in brainly.com/question/11149751
#LearnwithBrainly
